The theory presented in this paper is based on detailed matrix analysis with motivations
coming from the theory of differential equations, resp. from the oscillation theory of
linear Hamiltonian systems (REF ). It can be further developed in the direction of
the oscillation theory on discrete time domains [1]}, [2]} or
in the direction of singular comparison theorems for the oscillation numbers, as we
recently presented in [3]}, [4]} for conjoined bases of nonoscillatory
linear Hamiltonian systems. Such results may have fundamental applications in the theory
of Maslov index on unbounded intervals, or in the study of the rotation number of
a family of linear Hamiltonian systems, such as in [5]}, [6]}.
We also expect related research activity in the theory of matrices in general, for example
in the limit theorems for symmetric matrix valued functions generalizing the results in
[7]}, [8]} or [9]}.
